Comprehensive Oil Depletion Model Life-Cycle

Setting the Stage

In light of this fact, it should be no surprise that the possibility that world oil production will soon reach a peak and then inexorably decline is a subject of great interest and intense debate. As noted by Dr. Greene, the “pessimists,” a somewhat pejorative label given to those who are convinced that the oil peak is imminent and that its consequences will be dire, assert that world oil supply is chiefly determined by the geology of oil resources.

The term "pessimist" has no meaning anymore. Can you still call a person who questioned the run-up of hedge funds and derivatives, not to mention the stock market for the last 10+ years, a pessimist without incurring any sense of shame? All the models in that world got built to advance one motive -- that of profit, brought about by no small part greed. No one really cared whether they made sense in some theoretical framework, and why should they, since human nature would constantly batter down the model's premises in search of escape clauses. This occurred all in the nature of one-upping the next guy ... in a zero-sum game of zero-summed optimism.

So I have general agreement with "Dr.Greene" in that geology determines the oil depletion arc almost completely. I would even take it a step further and also claim that probability and statistics plays an even greater role. The following comprehensive framework, that has essentially described the information content of this blog the last few years, maps out what I have tried to achieve. Don't confuse this with any kind of wacked-out psychohistory-styled prediction of the future though. Although it shares some grand aspects of a statistics-based forecasting outlook, I think I know enough when to give it a rest and not to try to predict collective human actions.



I don't consider the math behind the models that difficult to understand. The two darkened bubbles above contain the mathematical foundation for parts of the discovery process along with the oil production model. Everything fits together like a glove (IMHO and after several years of effort) and the interpretations of the model replace a longstanding set of heuristics that in the past have served to cobble together a rather poorly-formed understanding of the aggregated oil production life-cycle. The last piece in the puzzle occurred in the past few months, as I tried to decipher a model for field-size distributions.

As I spent most of my time working my way backward in the oil life-cycle timeline (right to left in the above figure), I can't provide a linear description of the comprehensive model's development. In the interim, the following bullet list of links provides reference points for entry into a mind-blowing range of pessi-optimism or opto-pessimism ... depending on your point of view.

• "Dispersive Aggregation"
  
• "Dispersive Discovery"
  
• "Dispersive Reserve"
  
• "Oil Shock Model"
  
• "Derivation of the Logistic"
  
• "Hybrid Shock Model" (from the mind of Khebab)
  
• "Shocklets"
  

If you enjoy the art of rhetoric more than the dialectic, beware. For many, this stuff brings on MEGO, but for a few die-hards you can get your math-porn for free.

Investment in Knowledge

Nate Hagens over at TOD posted a brilliant comment in response to Exxon denial:

I am beginning to believe it is an advantage to NOT work in the oil industry to understand oil. These people have been wrong, are wrong, and are about to be VERY wrong with their understanding of what peak oil means. Peak Oil has many definitions, but the most common is the all time high in world annual production of crude oil. Resources have little to do with it. (There are probably 10 million earthworms on my property -but even with a team of people and the best equipment I might only get a fraction of them). Higher prices and higher technology have little to do with Peak Oil, which has to do with cheap, reliable flow rates. There is not the slightest evidence that market theories (or activities) has helped find any more oil and gas (in the United States) since price-induced drilling increases had essentially zero impact on the production (or finding) of oil and gas.

Lets scrap the word 'peak oil' for the moment. To the economists and cornucopians at Exxon, the API, the EIA, etc. I ask these questions:

1)Do you expect oil production costs to get cheaper over time?

2) Have we past the point of cheap oil? (which is what matters - who cares if we can get an extra 20 mbpd if it takes more energy, more steel, more water and costs $500 per barrel)

3)Will the energy and other resources you use to procure oil and natural gas increase or decrease in the future?

4)Irrespective of resource or reserves, what will be the highest, reasonably low priced (say under $80 cost), FLOW rate that you can consistently provide that is not subject to geopolitical disruptions at the margin? (i.e. is there a perpetual cushion in case something goes wrong)

5)What is the error band and confidence interval you assign to your above answers? Are you willing to stake the future of industrial civilization on your answers? Even if there is a 5% chance that the resources you see translate to regular, cheap, flow rates of high quality oil, that is too big of a risk for society to take (and I think it is much higher than that).

You people are asking the wrong questions, because you've been focused on what you believe is the most important aspect of the problem - where IS the oil. That is a small part of the many more important questions, yet the group think and myopia has created an enormous blindspot. A couple months ago, if I would have told you the Federal Reserve would DOUBLE its balance sheet since the end of September, would anyone have believed me? Well, they did. Rules and facts change. Correlations that worked in the past are now uncorrelated. What was uncorrelated in the past is now completely correlated. Thats why economics isn't science. Its based on a moving target. Economists at the oil companies are trained to think in resources and price, not in energy costs and externalities. They will not see this Black Swan until it bites them in the ass.

I don't believe in any kind of investment anymore besides an investment in knowledge. Forget investing in the stock market. Forget about investing in new ways to find oil and that "Drill, Baby, Drill" crap. Forget investing in any kind of investment, except for the one between our collective two ears.

USA Field Size Distribution

This dated paper (circa 1986) on USA oil field size has a few interesting statistics. I don't have any of the charts, but the authors roll up a few of the numbers from the curves.

The distribution of about 14,000 United States oil fields (Figure 2)--a partial sample of those in the lower 48 states--illustrates the importance of the larger fields. The sample includes almost all larger fields as known about 1970 and excludes many tiny fields as well as all of the more recent discoveries. The lower dotted line is made of 13,985 points representing the fields ordered according to increasing reserves size. Only 440 fields, or about 3%, are major ones larger than 50 million bbl. The upper curve tracks the percentage of the total oil volume occurring in fields greater than each size. From this curve, we read that the major fields, constituting only 3% of the total number, contain 80% of the total oil. Obviously, in this type of distribution one can account for the bulk of the oil by assessing the larger field possibilities only.

Selecting an effective minimum field-size cutoff is very important, because it affects every major factor in the assessment--the prospects to be counted and the success and risk levels, as well as the average field size. Normally, the minimum size is taken at or just below the assumed economic minimum for the area. This approach ensures that all prospects of real interest are included. It also avoids getting bogged down in hundreds or thousands of fields that are inconsequential to early exploration stages. Furthermore, the comparative data base for assessing sub-economic fields is very weak, as the true sizes of these fields have rarely been scaled. If desired, one can assess the small fields by statistical extrapolation or by estimating a lump-sum proportion from a volume curve like that of Figure 2.

Economic limits always truncate the lower ends of observed field-size distributions (Arps and Roberts, 1958; Kaufman et al, 1975; Grender et al, 1978; Drew et al, 1982; Vinkovetsky and Rokhlin, 1982). In nature's distribution, numbers of deposits probably increase progressively in successively smaller sizes down to droplets and molecules; such a distribution is not lognormal. But we deal exclusively with artificially truncated distributions whose plots almost invariably curve upward near the low-side truncation point (upper curve, Figure 3). Our United States distribution (lower curve, Figure 2) has no data below 1,000 bbl, and many of the data points below 10,000 bbl, where the graph ends, are questionable. If the plot were continued to the left, it would ultimately curve upward at t e point of economic truncation beyond which there are no data.

We use the computational convenience of the lognormal distribution, appropriately truncated, but would not argue that this scheme is better or worse than other computational ones for strongly right-skewed distributions that have many more little fields than big fields. Some investigators (e.g., Ivanhoe, 1976; Folinsbee, 1977; Coustau, 1980) plot field size bilogarithmically against rank order. For our assessment approach, we must normalize field numbers at this stage by plotting "percent greater than" against log size. Depending on purpose and data, we may express field size as recoverable volumes of oil or of gas, or of oil plus gas on an energy-equivalent basis.

These numbers (the 50Mb and the less than 0.1Mb) fill in the following points on the previous post.


The authors state that 3% of the highest rank of fields contain 80% of the oil, which includes rank up to 440 in this chart. Or this means that 20% of the oil resides in the lowest 97% of the rank.

U_p/U = (ln(1+Size/c) - 1/(1+Size/c)+ 1)/(ln(1+Max/c) - 1/(1+Max/c) + 1)

I would like to make sense of this but as I don't have the original charts, I am guessing as to whether the 80% makes sense. With the Dispersive Aggregation model for the extra 21,000 fields reported, the amount of oil contributed to those above 50Mb has dropped to 50%.

Year	Size	Fraction of Total	#Fields
1986	>50Mb	0.80	13,985
Today	>50Mb	0.51	34,969

In the last 20 years, we probably have gained a lot of extra mileage from the low volume fields, but I can't say for certain without filling in the historical data points. If someone can get a hold of this Baker paper and post some of the charts, it would help immensely.

These authors also believed that the field size distribution followed a log-normal. The Dispersive Aggregation mimics the general shape of the log-normal under certain regimes, especially under a wide variance, while at the same time generating the heavy Pareto-like tail (i.e. 1/x^p) that much of the data seems to indicate.


The following chart shows a cumulative field size distribution from the Canadian Williston Basin. The referenced article shows how they use a log-probability chart to map onto a log-normal curve; I pasted on a set of points corresponding to Dispersive Aggregation and as you can see, it mimics the behavior of a log-normal distribution.

Baker, R.A., H. M. Gehman, W. R. James, D. A. White, 1986,
Geologic Field Number and Size Assessment of Oil and Gas Plays,
in Oil and Gas Assessment: Methods and Applications: AAPG Studies in Geology
No. 21, p. 25 – 31.

Franken

Update: RECOUNT! The only reason I put up this post was that I knew it was going to be close, and Coleman is pure sleaze. I did an absentee and noticed that my ballot had ink already partially filled in the Senate column for one of the minor candidates. For once, I'd like to know if my vote got counted....

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For fellow Minnesotans reading this, vote Al Franken for Senate.

Norm Coleman is a corrupt, incompetent bureaucrat who has wasted precious intellectual resources pursuing the exaggerated "Oil for Food scandal" leading up to the Iraq war. Prior to the oil crunch this summer, Oil for Food was the closest that the Republicans ever got to even talking about the global oil situation, and it turned out to be a complete smoke-screen to cover their own interests. As the previous ranking member of the Permanent Subcommittee on Investigations, we can all blame Norm Coleman for running interference on one of the most effective head-fakes perpetrated in avoiding the truth. So much for investigatin' skills there, Norm

For fellow Wright County folks, I have no doubt you will say no to the imbecilic Michele Bachmann, in favor of the El-Train.